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Open boundaries for the nonlinear Schrödinger equation

✍ Scribed by A. Soffer; C. Stucchio

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
292 KB
Volume
225
Category
Article
ISSN
0021-9991

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✦ Synopsis

We present a new algorithm, the time dependent phase space filter (TDPSF) which is used to solve time dependent nonlinear Schro ¨dinger equations (NLS). The algorithm consists of solving the NLS on a box with periodic boundary conditions (by any algorithm). Periodically in time we decompose the solution into a family of coherent states. Coherent states which are outgoing are deleted, while those which are not are kept, reducing the problem of reflected (wrapped) waves. Numerical results are given, and rigorous error estimates are described.

The TDPSF is compatible with spectral methods for solving the interior problem. The TDPSF also fails gracefully, in the sense that the algorithm notifies the user when the result is incorrect. We are aware of no other method with this capability.

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